More about the Size Dependence of the Surface Energy of Charged Metal Clusters. Liquid Drop Model

V. V. Pogosov

Национальный университет «Запорожская политехника», ул. Жуковского, 64, 69063 Запорожье, Украина

Получена: 05.11.2023; окончательный вариант - 15.12.2023. Скачать: PDF

The problem of the sign of the size correction to the surface energy per unite area of a single charged metal nanocluster within the liquid-drop model (LDM) is considered. Within the stabilized jelly model detailing the LDM, the effective radii of the electron cloud for Cs, Na, Mg and Al clusters are estimated from the asymptotic behaviour of the electrical capacitance calculated by the Kohn–Sham method. The uncertainty of the cluster boundary associated with the atomic-scale roughness and nonsphericity of the surface, with taking into account the effective radius of the electron cloud of the cluster, can lead to an inversion of the sign of the size correction for surface tension. The distribution function of Cs clusters by charge and number of atoms in dense vapour on the saturation line is estimated. The fact that the surface energy of a metal depends on the dielectric constant as weighted average over the area of contact with the external environment is discussed. A metal droplet on a dielectric substrate and a droplet in its own dense vapour are discussed as appropriate contacts. The dependence of surface tension on electrical capacitance for Cs, Na, Mg, Pb, Au and Al is calculated. Contact of a droplet with a dielectric substrate always leads to a decrease in surface energy.

Ключевые слова: surface energy, metal nanocluster, electron-cloud radius, stabilized jelly model.

URL: https://mfint.imp.kiev.ua/ru/abstract/v46/i04/0289.html

PACS: 36.40.Wa, 41.20.Cv, 61.50.Lt, 68.03.Cd, 71.15.Nc, 82.60.Qr


ЦИТИРОВАННАЯ ЛИТЕРАТУРА
  1. R. C. Tolman, J. Chem. Phys., 17, No. 3: 333 (1949). Crossref
  2. J. G. Kirkwood and P. B. Buff, J. Chem. Phys., 17, No. 3: 338 (1949). Crossref
  3. A. I. Rusanov, Fazovyye Ravnovesiya i Poverkhnostnyye Yavleniya [Phase Equilibria and Surface Phenomena] (Leningrad: Khimiya: 1967) (in Russian).
  4. M. P. A. Fisher and M. Wortis, Phys. Rev. B, 29, No. 11: 6252 (1984). Crossref
  5. V. G. Baidakov and G. Sh. Boltachev, Phys. Rev. E, 59, No. 1: 469 (1999). Crossref
  6. J. W. P. Schmelzer, A. S. Abyzov, and V. G. Baidakov, Entropy, 21: 670 (2019). Crossref
  7. J. S. Rowlinson and B. Widom, Molecular Theory of Capillarity (Mineola, NY: Dover Publications: 2013).
  8. S. Burian, M. Isaiev, K. Termentzidis, V. Sysoev, and L. Bulavin, Phys. Rev. E, 95, No. 6: 062801 (2017). Crossref
  9. S. W. Cui, J.-A. Wei, Q. Li, W.-W. Liu, P. Qian, and X. S. Wang, Chinese Phys. B, 30, No. 1: 016801 (2021). Crossref
  10. W. Vogelsberger, H.-G. Fritsche, and E. Müller, Phys. Status Solidi (b), 148, No. 1: 155 (1988). Crossref
  11. H. Haberland, Clusters of Atoms and Molecules. Theory, Experiment, and Clusters of Atoms (Berlin: Springer: 1994). Crossref
  12. N. T. Gladkikh, L. K. Griogryeva, S. V. Dukarov, V. E. Zilbervarg, V. I. Larin, E. L. Nagaev, and S. P. Chizhik, Fizika Tverdogo Tela, 31, No. 5: 13 (1989) (in Russian).
  13. E. L. Nagaev, Uspekhi Fizicheskikh Nauk, 162, No. 9: 49 (1992) (in Russian). Crossref
  14. L. M. Shcherbakov and V. M. Samsonov, J. Surface Investigation. X-Ray, Synchrotron and Neutron Techniques, No. 3: 95 (1995) (in Russian).
  15. J. L. Martins, R. Car, and J. Buttet, Surf. Sci., 106, Nos. 1–3: 265 (1981). Crossref
  16. I. T. Iakubov, A. G. Khrapak, L. I. Podlubny, and V. V. Pogosov, Solid State Commun., 53, No. 4: 427 (1985). Crossref
  17. J. P. Perdew, Y. Wang, and E. Engel, Phys. Rev. Lett., 66, No. 4: 508 (1991). Crossref
  18. C. Fiolhas and J. P. Perdew, Phys. Rev. B, 45, No. 11: 6207 (1992). Crossref
  19. P. Ziesche, J. P. Perdew, and C. Fiolhais, Phys. Rev. B, 49, No. 12: 7919 (1994). Crossref
  20. V. V. Pogosov, Chem. Phys. Lett., 193, No. 6: 473 (1992). Crossref
  21. V. V. Pogosov, Solid State Commun., 89, No. 12: 1017 (1994). Crossref
  22. C. Hock, C. Bartels, S. Straßburg, M. Schmidt, H. Haberland, B. von Issendorff, and A. Aguado, Phys. Rev. Lett., 102, No. 4: 043401 (2009). Crossref
  23. D. Vollath, F. D. Fischer, and D. Holec, Beilstein J. Nanotechnol., 9: 2265 (2018). Crossref
  24. D. Holec, P. Dumitraschkewitz, D. Vollath, and F. D. Fischer, Nanomaterials, 10, No. 3: 484 (2020). Crossref
  25. P. Z. Pawlow, Z. phys. Chem., 65U, Iss. 1: 1, 545 (1909). Crossref
  26. A. V. Korotun and V. V. Pogosov, Phys. Solid State, 63, No. 1: 122 (2021). Crossref
  27. M. Itoh, V. Kumar, and Y. Kawazoe, Phys. Rev. B, 73, No. 3: 035425 (2006). Crossref
  28. S. Ali, V. S. Myasnichenko, and E. C. Neyts, Phys. Chem. Chem. Phys., 18, Iss. 2: 792 (2016). Crossref
  29. H. Haouas, L. El. Atouani, K. Sbiaai, and A. Hasnaoui, Comput. Mater. Sci., 214: 111695 (2022). Crossref
  30. S. Polsterová, M. Friák, M. Všianská, and M. Šob, Nanomaterials, 10, No. 4: 767 (2020). Crossref
  31. R. W. Hasse and W. D. Myers, Geometrical Relationships of Macroscopic Nuclear Physics (Springer-Verlag: 1988). Crossref
  32. W. A. de Heer, Rev. Mod. Phys., 65, No. 3: 611 (1993). Crossref
  33. M. Brack, Rev. Mod. Phys., 65, No. 3: 677 (1993). Crossref
  34. M. Seidl, J. P. Perdew, M. Brajczewska, and C. Fiolhais. J. Chem. Phys., 108, No. 19: 8182 (1998). Crossref
  35. K. K. Nanda, Phys. Lett. A, 376, No. 19: 1647 (2012). Crossref
  36. V. V. Pogosov and V. I. Reva, J. Chem. Phys., 148, No. 4: 044105 (2018). Crossref
  37. V. V. Pogosov and V. I. Reva, Phys. Solid State, 60, No. 4: 634 (2018). Crossref
  38. T. Gould, B. T. Liberles, and J. P. Perdew, J. Chem. Phys., 152, No. 5: 054105 (2020). Crossref
  39. V. V. Pogosov and A. G. Khrapak, Teplofizika Vysokikh Temperatur, 26, No. 2: 145 (1988) (in Russian).
  40. V. Fortov, I. Iakubov, and A. Khrapak, Physics of Strongly Coupled Plasma (Oxford: Oxford Academic Books: 2006), ch. 4. Crossref
  41. V. V. Pogosov, Phys. Solid State, 64, No. 1: 121 (2022). Crossref
  42. V. V. Pogosov, Phys. Met. Metallogr., 123, No. 1: 16 (2022). Crossref
  43. V. V. Pogosov, Metallofiz. Noveishie Tekhnol., 45, No. 8: 935 (2023). Crossref
  44. A. V. Babich and V. V. Pogosov, Phys. Solid State, 55, No. 1: 196 (2013). Crossref
  45. V. V. Pogosov, A. V. Babich, and P. V. Vakula, Phys. Solid State, 55, No. 10: 2120 (2013). Crossref